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zahrcast
This page belongs to the prostate cancer case study. It shows three checks on each fit: survival curves replicated from the fitted model next to the observed curves, the probability integral transform (PIT), which places each patient's observed time within that patient's replicated times, and the sampler's and effective sample sizes. Sia was fitted once at each cut-off, using only the data available at that date, and once to the full data. The controls below select the fit and apply to every chart on the page.
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Each replicate keeps the enrolled target-trial patients, their baseline covariates and their observed baseline burden, and draws a new burden trajectory, progression and death for each of them from the fitted model. A Kaplan-Meier curve is computed for each replicate. The band is the pointwise 80% interval of those curves at each week, and the line inside it is their median. The solid curve is the Kaplan-Meier curve observed in the same patients.
Two settings change how the replicates are drawn. With each patient's own effects, a replicate uses that patient's estimated patient-level effects. With effects redrawn from the population, it draws new patient-level effects from the fitted population distribution. An uncensored replicate follows each patient to the end of the forecast horizon. A replicate censored as observed stops each patient at the time the patient's observed record stops.
These replicates are not the forecasts on the case-study page. A forecast there keeps each patient's observed history and simulates only the time after it. A replicate here simulates every patient from enrollment, so the two sets of curves can differ for the same fit.
One chart per endpoint and arm. Time is months since each patient's enrollment. At a cut-off, the observed curve uses only the follow-up available at that date. The curve observed at the full data cut can be added for comparison when the replicates are uncensored.
The PIT places each patient's observed time within that patient's own replicated times. If the two come from the same distribution, the PIT values are uniform on 0 to 1 and each of the ten bins expects one tenth of the patients. The dashed line marks that count, and the shaded band is the 10th to 90th percentile of a bin's count when the values are uniform. Bars are split into patients with an event and censored patients for arms with at least 20 patients.
The control switches between versions of the PIT. In sample uses the fit and patient effects selected above, and that fit used each patient's own data. Leave one out predicts each patient from the full data fit reweighted to leave out that patient's data; its captions count patients by how reliable the weights are. How the PIT works explains each version step by step.
One histogram per endpoint and arm.
is the rank-normalized split , which compares the spread of the draws within each chain with the spread across chains. Bulk and tail ESS are effective sample sizes for the center and the tails of each distribution.
Each replicated KM row has one dot per replication setting, showing the largest and the smallest ESS over every arm and week of that setting's curves. The larger dot is the setting selected above. Each covariate row has one dot per covariate coefficient, on the per-SD scale, grouped by the part of the model it acts on. In the ESS panel, filled dots are bulk ESS and open dots are tail ESS. Dashed lines mark of 1.01 and 1.05 and ESS of 100 and 400. A tail ESS is undefined when a curve's draws are tied on a few values.